A nonmonotone line search technique for Newton's method
SIAM Journal on Numerical Analysis
A nonsmooth version of Newton's method
Mathematical Programming: Series A and B
Convergence analysis of some algorithms for solving nonsmooth equations
Mathematics of Operations Research
A semismooth equation approach to the solution of nonlinear complementarity problems
Mathematical Programming: Series A and B
Solution of monotone complementarity problems with locally Lipschitzian functions
Mathematical Programming: Series A and B - Special issue on computational nonsmooth optimization
A New Class of Semismooth Newton-Type Methods for Nonlinear Complementarity Problems
Computational Optimization and Applications
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part II
Associative and Jordan Algebras, and Polynomial Time Interior-Point Algorithms for Symmetric Cones
Mathematics of Operations Research
Smoothing Functions for Second-Order-Cone Complementarity Problems
SIAM Journal on Optimization
Computational Optimization and Applications
SIAM Journal on Optimization
Strong Semismoothness of the Fischer-Burmeister SDC and SOC Complementarity Functions
Mathematical Programming: Series A and B
An unconstrained smooth minimization reformulation of the second-order cone complementarity problem
Mathematical Programming: Series A and B
Cartesian P-property and Its Applications to the Semidefinite Linear Complementarity Problem
Mathematical Programming: Series A and B
A descent method for a reformulation of the second-order cone complementarity problem
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Computers & Mathematics with Applications
Neural networks for solving second-order cone constrained variational inequality problem
Computational Optimization and Applications
An application of a merit function for solving convex programming problems
Computers and Industrial Engineering
Information Sciences: an International Journal
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In this paper, we present a detailed investigation for the properties of a one-parametric class of SOC complementarity functions, which include the globally Lipschitz continuity, strong semismoothness, and the characterization of their B-subdifferential. Moreover, for the merit functions induced by them for the second-order cone complementarity problem (SOCCP), we provide a condition for each stationary point to be a solution of the SOCCP and establish the boundedness of their level sets, by exploiting Cartesian P-properties. We also propose a semismooth Newton type method based on the reformulation of the nonsmooth system of equations involving the class of SOC complementarity functions. The global and superlinear convergence results are obtained, and among others, the superlinear convergence is established under strict complementarity. Preliminary numerical results are reported for DIMACS second-order cone programs, which confirm the favorable theoretical properties of the method.